Gamma mixture of generalized error distribution

Abstract

A new symmetric heavy-tailed distribution, namely gamma mixture of generalized error distribution is defined by scaling generalized error distribution with gamma distribution, its probability density function, k-moment, skewness and kurtosis are derived. After tedious calculation, we also give the Fisher information matrix, moment estimators and maximum likelihood estimators for the parameters of gamma mixture of generalized error distribution. In order to evaluate the effectiveness of the point estimators and the stability of Fisher information matrix, extensive simulation experiments are carried out in three groups of parameters. Additionally, the new distribution is applied to Apple Inc. stock (AAPL) data and compared with normal distribution, F-S skewed standardized t distribution and generalized error distribution. It is found that the new distribution has better fitting effect on the data under the Akaike information criterion (AIC). To a certain extent, our results enrich the probability distribution theory and develop the scale mixture distribution, which will provide help and reference for financial data analysis.     

A hierarchical point process with application to storm cell modelling

In environmetrics, interest often centres around the development of models and methods for making inference on observed point patterns assumed to be generated by latent spatial or spatio‐temporal processes, which may have a hierarchical structure. In this research, motivated by the analysis of spatio‐temporal storm cell data, we generalize the Neyman–Scott parent–child process to account for hierarchical clustering. This is accomplished by allowing the parents to follow a log‐Gaussian Cox process thereby incorporating correlation and facilitating inference at all levels of the hierarchy. This approach is applied to monthly storm cell data from the Bismarck, North Dakota radar station from April through August 2003 and we compare these results to simpler cluster processes to demonstrate the advantages of accounting for both levels of correlation present in these hierarchically clustered point patterns. The Canadian Journal of Statistics 47: 46–64; 2019 © 2019 Statistical Society of Canada     

Ratio detection for mean change in α mixing observations

A ratio test based on the indicators of the data minus the sample median is proposed to detect the change in the mean of α-mixing stochastic sequences. The asymptotic distribution of the test is derived under the null hypothesis. The consistency of the proposed test is also obtained under the hypothesis that μ changes at some unknown time. We also propose a consistent estimator for the change point on the ratio test. Simulations demonstrate that the test and the estimator behaves well for heavy-tailed sequences. At last, an empirical application demonstrate the validity of the test and the estimator.     

Generalized fiducial inference for generalized exponential distribution

This article mainly considers interval estimation of the scale and shape parameters of the generalized exponential (GE) distribution. We adopt the generalized fiducial method to construct a kind of new confidence intervals for the parameters of interest and compare them with the frequentist and Bayesian methods. In addition, we give the comparison of the point estimation based on the frequentist, generalized fiducial and Bayesian methods. Simulation results show that a new procedure based on generalized fiducial inference is more applicable than the non-fiducial methods for the point and interval estimation of the GE distribution. Finally, two lifetime data sets are used to illustrate the application of our new procedure.     

The convex hull of a dependent vector-valued process

An important problem in the study of animal behaviour is the determination of home range. This set can be estimated by the convex hull of the location of an animal at successive time points. However, this estimate is based on a sample of highly dependent observations when the time intervals between fixes are small. In this paper we quantify the effect of dependence on various properties of the convex hull of several dependent point processes in the plane using Monte-Carlo methods. We compare our results with the independent case and make some comments on the asymptotic behaviour of this set.     

A Sequential Point Process Model and Bayesian Inference for Spatial Point Patterns with Linear Structures

Abstract. We introduce a flexible spatial point process model for spatial point patterns exhibiting linear structures, without incorporating a latent line process. The model is given by an underlying sequential point process model. Under this model, the points can be of one of three types: a ‘background point’ an ‘independent cluster point’ or a ‘dependent cluster point’. The background and independent cluster points are thought to exhibit ‘complete spatial randomness’, whereas the dependent cluster points are likely to occur close to previous cluster points. We demonstrate the flexibility of the model for producing point patterns with linear structures and propose to use the model as the likelihood in a Bayesian setting when analysing a spatial point pattern exhibiting linear structures. We illustrate this methodology by analysing two spatial point pattern datasets (locations of bronze age graves in Denmark and locations of mountain tops in Spain).     

Rank Preserved Aggregation Rules and Application to Reliability Allocation

The reliability allocation for computerized numerical control lathes can be seen as a MCDM problem. In a previous article (Hou, 2011 Hou , F. ( 2011 ). A Semiring-based study of judgment matrices: properties and models . Inform. Sciences 181 : 2166 – 2176 .[Crossref], [Web of Science ®] , [Google Scholar]), the fixed point equations corresponding to the priority vectors of consistent judgment matrices were given under semiring operations. The existence and uniqueness of the min-normalized fixed point were also proved. This article shows the application of the decision fixed point. First, fixed point-based aggregation rule with rank preservation is proposed for AHP. Then, counterpart results under a semiring isomorphism are presented for the FPR-AHP, where the preference information is presented by additive reciprocal judgment matrices (fuzzy preference relations). Third, the proposed aggregation rules are extended to the data incorporation of MCDM problems. Finally, application to the reliability allocation for computerized numerical control lathes is investigated.     

论中国现代文学史起点的"向前移"问题

"'五四'新文学运动"曾被视为中国现代文学史的"起点",这样就遮蔽了"五四"前中国文学现代化的实际进程,相应也忽视了"五四"前许多文学作品已经初具的现代性.从早期启蒙者身份的重新认定,在文学作品中对科学、人权的引进时序,中国期刊的三波现代化浪潮,早期白话文的倡导和早期翻译作品的成就等方面来看,有必要将中国现代文学史的起点"向前"位移,才能将20世纪文学作为一个不可分割的整体来加以把握.     

地价监测点的价格更新研究

城市地价监测点的价格更新是地价动态监测体系维护和更新的重要部分,从监测点地价的影响因素分析出发,采用多因素权重法建立监测点地价更新的数学模型,以专家确定影响因素权重和估价师对各因子变动比例打分的形式,掌握土地条件变化引起的地价动态变化,从而达到更加准确、方便、快捷更新监测点地价的目的。以重庆市江北区部分监测点为例证明此方法的可行性。     

Existence and Uniqueness of a Fixed Point for Local Contractions

This paper proves the existence and uniqueness of a fixed point for local contractions without assuming the family of contraction coefficients to be uniformly bounded away from 1. More importantly it shows how this fixed‐point result can apply to study the existence and uniqueness of solutions to some recursive equations that arise in economic dynamics.